The exact distribution of exogenous variable coefficient estimators (Q760725)

This paper derives the exact probability density function of the instrumental variable estimator of the exogenous variable coefficient vector in a structural equation containing \(n+1\) endogenous variables and N degrees of overidentification. The derivations make use of an operator calculus which simplifies the algebra of invariant polynomials with multiple matrix arguments. A leading case of the general distribution that is more amenable to analysis and computation is also presented. Conventional classical assumptions of normally distributed errors and non-random exogenous variables are employed.